Death and uncertainty: Bayesian modeling of the association between life span and reproductive investment in birds.

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Presented at the Ecological Society of Germany, Austria and Switzerland (GfÖ) 42nd annual meeting. Leuphana University Lüneburg, Germany. 10th-14th September 2012

Presented at the Ecological Society of Germany, Austria and Switzerland (GfÖ) 42nd annual meeting. Leuphana University Lüneburg, Germany. 10th-14th September 2012

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  • 1. Death and uncertainty: Bayesian modeling of the association between life span and reproductive investment in birds. Photo: bramblejungle/flickr Owen R. Jones* and Fernando Colchero Max Planck Institute for Demographic Research, Rostock *jones@demogr.mpg.de, website: owenjon.es11th September 2012, GfÖ, Lüneburg, Germany
  • 2. Grey partridge (Perdix perdix) Fulmar (Fulmarus glacialis)
  • 3. de Magalhaes & Costa 2009 J. Evol. Biol. Robinson 2005 BTO Research Report 407
  • 4. Data issues: sample size 30 25 Max. observed lifespan• Maximum observed life 20 span increases with sample size 15• Species with small sample 10 sizes are problematic 5 0 0 20 40 60 80 100 Sample size
  • 5. Data issues: truncation/censoringBirth/hatching Death
  • 6. Data issues: truncation/censoringBirth/hatching Death Truncation
  • 7. Data issues: truncation/censoringBirth/hatching Death Truncation Censoring
  • 8. Trait evolution‣ Closely related species tend to share similar trait values by inheritance (phylogenetic signal)‣ Traits can also be similar due to similar life style (convergent evolution)‣ Life history correlation can be due to influence of the trait in question, or simply an inherited characteristic.
  • 9. Aim• To develop and test a statistical modelling framework that accounts for these data issues while using phylogenic information.
  • 10. The data set• British Trust for Ornithology has carried out mark-capture-recovery since 1933• Maximum recorded life span for >200 species• Clutch size, number of broods, body mass Robinson 2005 BTO Research Report 407
  • 11. Bird illustrations: RSPB
  • 12. Cuckoo (Cuculus canorus)
  • 13. Phylogeny:Thomas, GH 2008 Proc. R. Soc. B
  • 14. Bird illustrations: RSPB
  • 15. Bird illustrations: RSPB
  • 16. Bird illustrations: RSPB
  • 17. Bird illustrations: RSPB
  • 18. Phylogenetic signal measures the amount thatphylogeny influences trait (0 - 1). Pagel’s Lambda for longevity ~ 0.73
  • 19. Ordinary least squares regression 50 20Life span (yrs) 10 5 2 5 50 500 5000 1 2 5 10 20 Weight (g) Effort (clutch size * broods)
  • 20. Ordinary least squares regression 50 20Life span (yrs) 10 5 2 5 50 500 5000 1 2 5 10 20 Weight (g) Effort (clutch size * broods) R2 = 0.26 R2 = 0.27
  • 21. Phylogenetic correction Independent contrasts Assumes Lambda = 1 50 20Life span (yrs) 10 5 2 5 50 500 5000 1 2 5 10 20 Weight (g) Effort (clutch size * broods) R2 = 0.26 to <0.01 R2 = 0.27 to <0.01
  • 22. Phylogenetic correction Independent contrasts Optimised PGLS Assumes Lambda = 1 Lambda = 0.73 50 50 20 20Life span (yrs) Life span (yrs) 10 10 5 5 2 2 5 50 500 5000 1 2 5 10 20 5 50 500 5000 1 2 5 10 20 Weight (g) Effort (clutch size * broods) Weight (g) Effort (clutch size * broods) R2 = 0.26 to <0.01 R2 = 0.27 to <0.01 R2 = 0.26 to 0.06 R2 = 0.27 to 0.07
  • 23. Phylogenetic correction Independent contrasts Optimised PGLS Assumes Lambda = 1 Lambda = 0.73 50 50 20 20Life span (yrs) Life span (yrs) 10 10 5 5 2 2 5 50 500 5000 1 2 5 10 20 5 50 500 5000 1 2 5 10 20 Weight (g) Effort (clutch size * broods) Weight (g) Effort (clutch size * broods) R2 = 0.26 to <0.01 R2 = 0.27 to <0.01 R2 = 0.26 to 0.06 R2 = 0.27 to 0.07 Can we improve the fit by accounting for data problems?
  • 24. Bayesian state-space model Process model Predictor Observed Response X Y Phylogeny
  • 25. Bayesian state-space model Process model Predictor Observed Response X Y Phylogeny Data model •Sample size •Censoring True Response •Truncation Y*
  • 26. Bayesian state-space modelMaximise likelihood of both Process model • MCMC framework Predictor Observed Response • Simultaneously estimates: X Y • Coefficients of process model Phylogeny • Phylogenetic signal • True response Data model • Error in process model • Error in data model •Sample size • -> Degree of censoring, •Censoring True Response truncation and sample size •Truncation Y* effects.
  • 27. State-space regression models 50 20Life span (yrs) 10 5 2 5 50 500 5000 1 2 5 10 20 Weight (g) Effort (clutch size * broods) R2 = 0.06 to 0.10 R2 = 0.07 to 0.12
  • 28. BTO data underestimates lifespan for many species 1000 800 % difference in life span 600 400 200 0 0 5 10 15 20 Effort
  • 29. BTO data underestimates lifespan for many species 1000 800 % difference in life span 600 400 200 0 0 5 10 15 20 Effort
  • 30. Conclusions• Life history patterns are moderated by phylogeny - we can use this information• Method of correction is fundamentally important (i.e. evolutionary model assumed)• Data issues can be solved• Further analyses are in the pipeline!
  • 31. We have a new R package!! To estimate survival/mortality trajectories from capture-mark- recapture data.http://basta.r-forge.r-project.org